Symmetric tensor networks for 2d quantum matter

• Applicant: Professor Dr. Matteo Rizzi, since 9/2018
• Subject Area: Theoretical Condensed Matter Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2017 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 358346317

• Final Report Year: 2020

Final Report Abstract

This DFG project allowed us to develop new methods to solve long-standing open problems in 2d condensed matter physics which are key in our understanding of quantum matter. It allowed us to implement new general-purpose numerical methods for 2d systems with nonabelian symmetries. Introducing non-abelian symmetries in the game has been a challenge, but brought unprecedented accuracy to calculations. The project has consolidated new tensor network tools in the study of 2d quantum matter. The produced numerical toolbox, which we plan to deploy open-source in the coming future, has a long-standing impact in fields such as condensed matter physics, quantum-atom optics, lattice gauge theory, quantum information, quantum chemistry, and computational physics.

Publications

• “Quantum criticality on a chiral ladder: an SU(2) iDMRG study”, Phys. Rev. B 99, 205121 (2019)
  P. Schmoll, A. Haller, M. Rizzi, R. Orus
  (See online at https://doi.org/10.1103/physrevb.99.205121)
• “A programming guide for tensor networks with global SU(2) symmetry”, Annals of Physics 419 (2020) 168232
  P. Schmoll, S. Singh, M. Rizzi, R. Orus
  (See online at https://doi.org/10.1016/j.aop.2020.168232)
• “Benchmarking global SU(2) symmetry in 2d tensor network algorithms”
  P. Schmoll, R. Orus
  (See online at https://doi.org/10.1103/PhysRevB.102.241101)
• “Fine-grained tensor network methods”, Phys. Rev. Lett. 124, 200603 (2020)
  P. Schmoll, S. S. Jahromi, M. Hörmann, M. Mühlhauser, K. P. Schmidt, R. Orus
  (See online at https://doi.org/10.1103/physrevlett.124.200603)